This study focuses on improving a word embedding model to enhance the performance of downstream tasks, such as those of dialog systems. To improve traditional word embedding models, such as skip-gram, it is critical to refine the word features and expand the context model. In this paper, we approach the word model from the perspective of subword embedding and attempt to extend the context model by integrating various sentence models. Our proposed sentence model is a subword-based skip-thought model that integrates self-attention and relative position encoding techniques. We also propose a clustering-based dialog model for downstream task verification and evaluate its relationship with the sentence-model-based subword embedding technique. The proposed subword embedding method produces better results than previous methods in evaluating word and sentence similarity. In addition, the downstream task verification, a clustering-based dialog system, demonstrates an improvement of up to 4.86% over the results of FastText in previous research.